Wednesday defender Graeme Lee struck in injury-time to end Bristol City's run of 11 successive wins.
Lee, making his comeback after injury, headed home at the far post following a
long throw from Leigh Bromby.
Wednesday saw a strong penalty appeal rejected before half-time when Danny Coles appeared to handle the ball.
Coles almost gave City the lead with a second-half header which hit the underside of the bar while Jon Shaw missed a late header for the Owls.
Sheff Wed: Pressman, Dean Smith, Lee, Wood, Bromby, Quinn, Haslam, Chambers, Barry-Murphy, Shaw, Ndumbu-Nsungu. Subs: Poulter, Beswetherick, Wilson, Needham, McMahon.
Bristol City: Phillips, Carey, Butler, Coles, Hill, Wilkshire, Doherty, Tinnion, Aaron Brown, Peacock, Miller. Subs: Burnell, Goodfellow, Roberts, Woodman, Lita.
Referee: M Cowburn (Lancashire)